IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i18p3243-d908650.html
   My bibliography  Save this article

Geometric Studies on Mittag-Leffler Type Function Involving a New Integrodifferential Operator

Author

Listed:
  • F. Ghanim

    (Department of Mathematics, College of Science, University of Sharjah, Sharjah P.O. Box 27272, United Arab Emirates)

  • Hiba F. Al-Janaby

    (Department of Mathematics, College of Science, University of Baghdad, Baghdad 10071, Iraq)

  • Marwan Al-Momani

    (Department of Mathematics, College of Science, University of Sharjah, Sharjah P.O. Box 27272, United Arab Emirates)

  • Belal Batiha

    (Department of Mathematics, Faculty of Science and Information Technology, Jadara University, Irbid 21110, Jordan)

Abstract

The generalized exponential function in a complex domain is called the Mittag-Leffler function (MLF). The implementations of MLF are significant in diverse areas of science. Over the past few decades, MLF and its analysis with generalizations have become an increasingly rich research area in mathematics and its allied fields. In the geometric theory of meromorphic functions, the main contribution to this discipline of study is to enrich areas of operator theory on complex punctured domains and differential complex inequalities, namely, subordination theory. This effort presents integrodifferential operator of meromorphic functions in the punctured unit disk. It is formulated by combining the differential operator and the integral operator correlating with the extended generalized Mittag-Leffler function. Furthermore, some interesting geometric features in terms of the subordination principle are investigated.

Suggested Citation

  • F. Ghanim & Hiba F. Al-Janaby & Marwan Al-Momani & Belal Batiha, 2022. "Geometric Studies on Mittag-Leffler Type Function Involving a New Integrodifferential Operator," Mathematics, MDPI, vol. 10(18), pages 1-10, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:18:p:3243-:d:908650
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/18/3243/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/18/3243/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Rakesh K. Parmar, 2015. "A Class of Extended Mittag–Leffler Functions and Their Properties Related to Integral Transforms and Fractional Calculus," Mathematics, MDPI, vol. 3(4), pages 1-14, November.
    2. Firas Ghanim & Khalifa Al-Shaqsi & Maslina Darus & Hiba Fawzi Al-Janaby, 2021. "Subordination Properties of Meromorphic Kummer Function Correlated with Hurwitz–Lerch Zeta-Function," Mathematics, MDPI, vol. 9(2), pages 1-10, January.
    3. Hiba Al-Janaby & Firas Ghanim & Maslina Darus, 2020. "On The Third-Order Complex Differential Inequalities of ξ -Generalized-Hurwitz–Lerch Zeta Functions," Mathematics, MDPI, vol. 8(5), pages 1-21, May.
    4. Aabed Mohammed & Maslina Darus, 2011. "Starlikeness Properties of a New Integral Operator for Meromorphic Functions," Journal of Applied Mathematics, Hindawi, vol. 2011, pages 1-8, July.
    5. Hari M. Srivastava & Arran Fernandez & Dumitru Baleanu, 2019. "Some New Fractional-Calculus Connections between Mittag–Leffler Functions," Mathematics, MDPI, vol. 7(6), pages 1-10, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Alina Alb Lupaş, 2023. "Fuzzy Differential Subordination and Superordination Results for Fractional Integral Associated with Dziok-Srivastava Operator," Mathematics, MDPI, vol. 11(14), pages 1-20, July.
    2. Faten Fakher Abdulnabi & Hiba F. Al-Janaby & Firas Ghanim & Alina Alb Lupaș, 2023. "Some Results on Third-Order Differential Subordination and Differential Superordination for Analytic Functions Using a Fractional Differential Operator," Mathematics, MDPI, vol. 11(18), pages 1-14, September.
    3. Jordanka Paneva-Konovska, 2022. "Taylor Series for the Mittag–Leffler Functions and Their Multi-Index Analogues," Mathematics, MDPI, vol. 10(22), pages 1-15, November.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Oscar Martínez-Fuentes & Fidel Meléndez-Vázquez & Guillermo Fernández-Anaya & José Francisco Gómez-Aguilar, 2021. "Analysis of Fractional-Order Nonlinear Dynamic Systems with General Analytic Kernels: Lyapunov Stability and Inequalities," Mathematics, MDPI, vol. 9(17), pages 1-29, August.
    2. Dumitru Baleanu & Arran Fernandez, 2019. "On Fractional Operators and Their Classifications," Mathematics, MDPI, vol. 7(9), pages 1-10, September.
    3. Georgia Irina Oros, 2022. "Geometrical Theory of Analytic Functions," Mathematics, MDPI, vol. 10(18), pages 1-4, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:18:p:3243-:d:908650. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.